How to rename uploaded files

Sometimes, I think it would be advantageous to be able delete a previously uploaded file, then reupload that same file with the same name and have the same URL. WordPress.com, however, will automatically rename the new file, adding a number to its name. For example, deleting example-image.jpg and then reuploading it will cause it to be renamed as example-image1.jpg. Deleting that image and reuploading it will cause it to be renamed as example-image2.jpg, and so on. This is problematic because it causes broken links, and can be a pain to fix if the file is linked to in multiple locations. As far as I can tell, it occurs with all files: images, PDFs, audio files, and any other file type allowed on WordPress.com

According to designsimply, you won't ever be able to upload a new file with the same URL on WordPress.com.

But, according to Jane Wells, you can change the file URL when you upload a file.

So who's right? (Please let it be Jane Wells!) If you can change a file's URL when you upload it, how do you do it?